Anis Chelbi

Spare provisioning strategy for preventively replaced systems subjected to random failure

Abstract A jointly optimal periodic replacement and spare parts provisioning strategy is discussed. This strategy is completely defined once the replacement period T, the replenishment cycle R=kT (k=1, 2, …) , and the ordering point s are determined. The optimal strategy (T * , R * , s * ) , if it exists, is one which minimizes the total expected cost (replenishment cost+spare parts inventory management cost) per time unit over an infinite span. A numerical algorithm is proposed to find the optimal strategy. The system lifetime distribution, the probability distribution of the demand during the lead-time and the costs associated to the replenishment and the spare parts inventory management are supposed to be known. Some numerical results are presented.

Modeling and optimizing a joint inventory control and preventive maintenance strategy for a randomly failing production unit: Analytical and simulation approaches

This paper presents a joint optimal inventory control and preventive maintenance strategy for a randomly failing production unit which supplies an assembly line operating according to a just-in-time configuration. The production unit is submitted to a maintenance action as soon as it reaches a certain age T or at failure; whichever occurs first. In order to palliate perturbations caused by breakdowns and by planned maintenance actions both with random durations, a buffer stock is built up to ensure the supply of the assembly line at a constant rate. A mathematical model is developed to evaluate the average cost per time unit of the proposed strategy. Due to the complexity of the mathematical model and to some approximation assumptions, a second approach based on simulation and experimental design is developed. It allows us to simulate the proposed policy and to generate a second order response surface for easy computation of the optimal values of the decision variables which are the age T at which preventive maintenance must be performed, and the buffer stock level h.

An optimal inspection strategy for randomly failing equipment

Abstract This paper addresses the problem of generating optimal inspection strategies for randomly failing equipment where imminent failure is not obvious and can only be detected through inspection. Inspections are carried out following a condition-based procedure. The equipment is replaced if it has failed or if it shows imminent signs of failure. The latter state is indicated by measuring certain predetermined control parameters during inspection. Costs are associated with inspection, idle time and preventive or corrective actions. An optimal inspection strategy is defined as the inspection sequence minimizing the expected total cost per time unit over an infinite span. A mathematical model and a numerical algorithm are developed to generate an optimal inspection sequence. As a practical example, the model is applied to provide a machine tool operator with a time sequence for inspecting the cutting tool. The tool life time distribution and the trend of one control parameter defining its actual condition are supposed to be known.

Integrated model of preventive maintenance, quality control and buffer sizing for unreliable and imperfect production systems

In this paper, we develop a joint quality control and preventive maintenance policy for a randomly failing production system producing conforming and non-conforming units. The considered system consists of one machine designed to fulfil a constant demand. According to the proportion l of non-conforming units observed on each lot and compared to a threshold value lm, one decides to undertake or not maintenance actions on the system. In order to palliate perturbations caused by the stopping of the machine to undergo preventive maintenance or an overhaul, a buffer stock h is built up to ensure the continuous supply of the subsequent production line. A mathematical model is developed and combined with simulation in order to determine simultaneously the optimal rate, and the optimal size h* which minimize the expected total cost per time unit including the average costs related to maintenance, quality and inventory.

Joint optimal inventory control and preventive maintenance policy

This paper investigates an integrated strategy of inventory control and preventive maintenance for a randomly failing production unit subject to a minimum required availability level. The production unit is submitted to a maintenance action as soon as it reaches a certain age m or at failure, whichever occurs first. A buffer stock h is built up at time A from the start of a production cycle in order to allow a continuous supply of the subsequent production unit at a constant rate during repair and preventive maintenance actions whose respective durations are random. A mathematical model and a numerical procedure are developed to find simultaneously the optimal values of the three decision variables (m*, h*, A*) which minimize the total average cost per time unit and satisfy the availability constraint.

Optimal selective renewal policy for systems subject to propagated failures with global effect and failure isolation phenomena

This paper considers a selective maintenance policy for multi-component systems for which a minimum level of reliability is required for each mission. Such systems need to be maintained between consecutive missions. The proposed strategy aims at selecting the components to be maintained (renewed) after the completion of each mission such that a required reliability level is warranted up to the next stop with the minimum cost, taking into account the time period allotted for maintenance between missions and the possibility to extend it while paying a penalty cost. This strategy is applied to binary-state systems subject to propagated failures with global effect, and failure isolation phenomena. A set of rules to reduce the solutions space for such complex systems is developed. A numerical example is presented to illustrate the modeling approach and the use of the reduction rules. Finally, the Monte-Carlo simulation is used in combination with the selective maintenance optimization model to deal with a number of successive missions.

Simultaneous determination of production lot size and preventive maintenance schedule for unreliable production system

Purpose – The purpose of this study is to propose and model an integrated production‐maintenance strategy for unreliable production systems producing conforming and non‐conforming items.Design/methodology/approach – The proposed integrated policy is defined and modeled mathematically.Findings – The paper focuses on finding simultaneously the optimal values of the lot size Q and the age T at which preventive maintenance must be performed. These values minimize the total average cost per time unit over an infinite horizon.Practical implications – The paper attempts to integrate in a single model the three main aspects of any manufacturing system: production, maintenance, and quality. It deals with the lot‐sizing problem for a production system which may randomly shift to an out‐of‐control state and produce non‐conforming units. The system is submitted to an age‐based preventive maintenance policy. The effect of performing preventive maintenance on quality‐ and inventory‐related costs is shown through a nume...

Generalized inspection strategy for randomly failing systems subjected to random shocks

Abstract This paper is motivated by the study of randomly failing systems whose state is only known through inspection and for which high availability is required. Security and alarm systems such as power system protective relays and environmental censoring equipment are typical examples of such systems. The deterioration process of these systems is generally governed by electromechanical transient shocks which occur randomly over time and whose magnitude is also random. These shocks damage the system cumulatively. Under the proposed inspection strategy, the system is inspected at predetermined times T 1 , T 2 , … . If failure is detected then the system is replaced by a new one, otherwise it is kept operating. The expression of the system time-stationary availability is developed and a numerical procedure is proposed to generate the inspection sequence which insures a preselected availability level. In cases where limited resources restrict the user to predetermined inspection period, the computer program generates the optimal design and operating parameters which will provide the targeted system availability level. A test case is analyzed and potential applications related to automotive and electronics industry are mentioned.

Contribution of simulation to the optimization of maintenance strategies for a randomly failing production system

This paper compares two strategies for operating a production system composed of two machines working in parallel and a downstream inventory supplying an assembly line. The two machines, which are prone to random failures, undergo preventive and corrective maintenance operations. These operations with a random duration make the machines unavailable. Moreover, during regular subcontracting operations, one of these machines becomes unavailable to supply the downstream inventory. In the first strategy it is assumed that the periodicity of preventive maintenance operations and the production rate of each machine are independent. The second strategy suggests an interaction between the periods of unavailability and the production rates of the two machines in order to minimize production losses during these periods. A simulation model for each strategy is developed so as to be able to compare them and to simultaneously determine the timing of preventive maintenance on each machine considering the total average cost per time unit as the performance criterion. The second strategy is then considered, and a multi-criteria analysis is adopted to reach the best cost-availability compromise.

Joint Quality Control and Preventive Maintenance Strategy for Imperfect Production Processes

In this paper, we develop a joint quality control and preventive maintenance policy for a production system producing conforming and nonconforming units. The considered system consists of one machine which must supply another production line operating on a just-in-time basis. Each lot produced by the machine is subject to a quality control. According to the proportion l of nonconforming units observed and compared to a threshold value lm, one decides to undertake or not maintenance actions on the system. In order to palliate perturbations caused by the stopping of the machine for preventive and corrective maintenance actions of random durations, a buffer stock h is built up to ensure the continuous supply of the subsequent production line. The proposed strategy is modelled using simulation and experimental design. This approach allows to generate a second order response surface allowing to easily determine the optimal rate,